Very few receivers of electromagnetic signals can operate in an ideal way, in the sense that the output of the signal reception stage would only consist of meaningful parts of the actual signal to be received. In practically all cases the receiver will simultaneously receive also unwanted signals, such as simultaneous transmissions from others than the source of the desired signal, as well as random noise. Also components of the receiver itself generate noise, which is summed to the actual signals at the output of the reception stage. The problem of separating the desired signal from noise has certain universal, commonly applicable features regardless of what purpose (e.g. communications, remote sensing, etc.) the signal serves.
The traditional approach to separating the desired signal from noise at the reception stage is based on filtering. For example, if a carrier frequency of the desired signal is known, the receiver may use a band pass filter to reject signals at frequencies that differ from the known carrier frequency more than half the width of a relatively narrow pass band. Filtering in the time space means only qualifying receiver output that occurs within a time interval that is known (or assumed) to correspond to the desired signal. Matched filters are devices that correlate the received signal with some code that is known to occur in the desired transmission, and so on. However, some noise will always have characteristics similar to those of the desired signal with certain accuracy, and hence despite all filtering, the output of the reception stage will always contain also unwanted signal components. The problem is prominent especially if the energy levels associated with the desired signal are low compared to the levels of coincident noise energy.
As an example we will consider the detection of relatively small, relatively faraway objects such as space debris with a radar. The transmitter of an ionospheric radar emits an electromagnetic transmission, usually a regularly repeated short pulse train, into a measurement direction pointing to the sky. A radar receiver receives echoes, which are the results of scattering of the transmission by meteors, space debris, and other targets that are capable of interacting with electromagnetic radiation at the frequency in use. Space debris comes in sizes ranging from dust and paint flakes to complete bodies of obsolete satellites. For the purposes of the present invention the smaller end of the size scale is the most important, because of the large number (hundreds of thousands) and the difficult detectability of small man-made objects orbiting the Earth. It is easy to understand that a radar echo produced by an object only some centimetres across at the distance of several hundreds or even thousands of kilometres can not be very powerful compared to measurement noise, even if very large (tens of metres in diameter) parabolic antennas are used.
FIG. 1 illustrates schematically an arrangement, in which a radar station 101 has made measurements of the sky above. Each black dot represents an individual measurement. Depending on the characteristics of the radar receiver, the signal processing capability, and the algorithms available, each measurement may represent a combination of different measured quantities. Typical quantities to be obtained as raw data are the round-trip delay it took for the transmission to be transmitted, scattered, and received; as well as the Doppler shift that the scattering target caused. From these the range (distance between the radar station and the target that caused the echo), radial velocity, and radial acceleration of the target can be calculated. The term “radial” refers to the direction of the straight line combining the radar and the scattering target. Radars equipped with monopulse feeds, as well as phased array systems, are also capable of measuring the angle or arrival from a point target.
We assume that during the time interval under examination, exactly one solid object orbiting the Earth has crossed the antenna beam. Some of the detected echoes were actually caused by said solid object, while the others are false echoes that represent either actual scattering of the radar transmission but by non-orbiting objects (such as meteors), or simply noise. The white dots marked with a vertical uncertainty bar are the actual target-related measurements in FIG. 1, and the curve 102 represents its orbit around the Earth. The problem is to decide, which of the (potentially very large number of) measurements should actually be taken into account as representing the orbiting object. Each dot in FIG. 1 is drawn with a velocity vector that represents the velocity that can be read from the radar measurement for the corresponding echo. It is intuitively very easy to understand that the velocity vectors of the echoes related to the actual orbiting target follow quite closely its orbit and are relatively close to each other in magnitude, while the velocity vectors of the other echoes may have any arbitrary direction and magnitude.
Combining multiple measurements of a moving target into one unified description of the target in terms of trajectory is a common problem in remote sensing. A wide variety of methods exists for solving this problem. Perhaps the most commonly used method is the so called detection threshold method, which relies on the fact that when a signal is strong enough compared to the noise level, it has to be a target with a very high probability. However, this approach suffers from several shortcommings. It cannot cope very well with active radar jamming, and it cannot be used to detect weaker targets, as the false alarm rate would be too large.
FIG. 2 illustrates schematically a similar problem that occurs in communications. A transmitting device 201 uses original data 202 to produce a transmission, which it emits in the form of a modulated electromagnetic carrier wave signal towards a receiving device 203. In order to find out the payload contents of the transmission, the receiving device 203 produces a series 204 of measurements that reflect what was received. Each individual measurement may contain values of one or more quantities such as phase, amplitude, and/or frequency. Again, only some of the measurements at the receiving device 203 are actually associated with the original transmission, while others represent interference or noise. Again, for example if the transmitting device wanted to conceal its transmission among noise to avoid detection by hostile parties, it may be difficult for the receiving device to decide, which measurements it should take into account for reconstructing the original data.